Non-invasive cardiac output determination

ABSTRACT

A method of controlling a gas delivery apparatus including an apparatus controllable variable using an iterative algorithm to deliver a test gas (TG) for non-invasively determining a subject&#39;s pulmonary blood flow comprising iteratively generating and evaluating test values of a iterated variable based on an iterative algorithm in order output a test value of the iterated variable that meets a test criterion wherein iterative algorithm is characterized in that it defines a test mathematical relationship between the at least one apparatus controllable variable, the iterated variable and an end tidal concentration of test gas attained by setting the apparatus controllable variable, such that the iterative algorithm is determinative of whether iteration on the test value satisfies a test criterion or iteratively generates a progressively refined test value.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a Continuation of U.S. application Ser. No.13/697,768, filed Jan. 16, 2013, which is national phase filing, under35 U.S.C. § 371(c), of International Application No. PCT/CA2011/000577,filed May 18, 2011, the disclosures of which are incorporated herein byreference in their entireties. International Application No.PCT/CA2011/000577, in turn, claims the benefit, under 35 U.S.C. §119(e), of U.S. provisional application Ser. No. 61/345,952, filed onMay 18, 2010, the disclosure of which is incorporated herein byreference in its entirety.

FIELD OF THE INVENTION

The present invention relates to a novel method for non-invasivelymeasuring pulmonary blood flow, to a novel method for controlling a gasdelivery apparatus and to a system and apparatus for implementing themethods.

BACKGROUND OF THE INVENTION

Many methods have been developed which attempt to measure pulmonaryblood flow without invasive access to the circulation ({dot over (Q)}).These methods, and their corresponding limitations, have beenexhaustively reviewed in the literature [1]. What emerges from thesereviews, however, are the potential benefits of non-invasive pulmonaryblood flow monitoring and the current lack of an adequate method.

Fick described the relationship between the blood gas concentrations andthe minute volume of expired gases during steady state [2].Specifically, if the amount of CO₂ in the lung is not changing, the fluxof CO₂ between the pulmonary capillary blood and the alveolar space isequal to the minute volume of expired CO₂ ({dot over (V)}CO₂). The fluxof CO₂ between the blood and the lungs can be calculated from theproduct of the pulmonary blood flow and the difference between the CO₂concentration in the mixed-venous blood (CvCO₂) entering the pulmonarycirculation and the corresponding concentration in the arterializedblood (CaCO₂) leaving the pulmonary circulation. The Fick mass balancerelation is shown in equation 1.

{dot over (V)}CO₂={dot over (Q)}(CvCO₂—CaCO₂)  (eq.1)

If the steady state minute volume of expired CO₂, arterial CO₂concentration, and mixed-venous CO₂ concentration can be determined,then the pulmonary blood flow can be calculated from equation 1.Conventionally, the minute volume of expired CO₂ is calculated from bagcollection of the expired breath, the product of the minute ventilationand the concentration of CO₂ in the mixed-expired gas, or integration ofthe instantaneous concentration of CO₂ at the mouth weighted by theinstantaneous flow. The partial pressure of CO₂ in the arterial blood isassumed to be equal to the end-tidal partial pressure of CO₂ and thenconverted to a concentration via the CO₂ dissociation curve ofoxygenated whole blood [3,4]. Traditionally, two methods have been usedto estimate the mixed-venous concentration of CO₂ for the purpose ofpulmonary blood flow measurement. The first method was presented byDefares [5]; the method of Collier [6] was published shortly thereafter.

In the method described by Defares, rebreathing is executed from a bagwith a low initial concentration of CO₂. As rebreathing proceeds, thelevel of CO₂ in the bag and the lung exponentially approach that in themixed-venous blood. However, equilibration of the bag and the lung withthe mixed-venous blood is slow as the volume of gas in the functionalresidual capacity is large. As a result, equilibration does not usuallyoccur before the change in the arterial CO₂ induced by rebreathingrecirculates back to the lung. The steady state mixed-venous CO₂—theasymptote of the exponential rise in end-tidal CO₂—must therefore becalculated from fitting an exponential curve to the end-tidal CO₂ of thebreaths during rebreathing prior to recirculation.

In the method introduced by Collier, rebreathing is executed from a bagwith an initial concentration of CO₂ slightly above an estimatedmixed-venous CO₂ concentration. The initial CO₂ in the bag is intendedto, upon inhalation, eliminate the CO₂ diffusion gradient between thefunctional residual capacity and the mixed-venous blood on the firstbreath of rebreathing. The equilibrium between the mixed-venous bloodand the alveolar space is recognized by the presence of a plateau in theend-tidal CO₂ during rebreathing.

As a variant of these rebreathing methods, Gedeon described a partialCO₂ rebreathing method for measuring pulmonary blood flow [7]. Partialrebreathing differs from the full rebreathing methods of Defares andCollier in that the entire tidal volume is not composed of rebreathedgas. Partial rebreathing is implemented by introducing a serial deadspace into the breathing circuit to increase the volume of rebreathedgas in each breath [8].

Partial rebreathing increases the average CO₂ content of the inspiredgas so that the flux of expired CO₂ is reduced. As a result, thealveolar and arterial CO₂ concentrations rise towards the level at whichthe flux of CO₂ between the blood and the lung will once again equal theexpired flux. Like the method of Defares, equilibration duringrebreathing may not occur before recirculation. Nevertheless, the Fickmass balance relation is applied at the end of rebreathing as shown inequation 2.

{dot over (V)}CO′₂={dot over (Q)}(CvCO₂—CaCO′₂)  (eq. 2)

Two steady states can be solved for the pulmonary blood flow and themixed-venous concentration of CO₂, revealing the differential Fickequations shown in equations 3a1 and 3b1.

$\begin{matrix}{\overset{.}{Q} = \frac{{\overset{.}{V}{CO}_{2}^{\prime}} - {\overset{.}{V}{CO}_{2}}}{{CaCo}_{2} - {CaCO}_{2}^{\prime}}} & \left( {{{eq}.\mspace{14mu} 3}{a1}} \right) \\{{C\overset{\_}{v}{CO}_{2}} = \frac{{{{CaCO}_{2} \cdot \overset{.}{V}}{CO}_{2}^{\prime}} - {{{CaCO}_{2}^{\prime} \cdot \overset{.}{V}}{CO}_{2}}}{{\overset{.}{V}{CO}_{2}^{\prime}} - {\overset{.}{V}{CO}_{2}}}} & \left( {{{eq}.\mspace{14mu} 3}{b1}} \right)\end{matrix}$

In practice, fluctuations in alveolar ventilation induce perturbationsin the instantaneous flux of expired CO₂ and in arterial CO₂ levels,leading to significant errors in calculating pulmonary blood flow. Thiserror is pronounced in untrained spontaneous breathers [9].

In the method of Defares specifically, the mixed-venous concentration ofCO₂ is extrapolated from the exponential rise in the end-tidal CO₂measured during rebreathing before recirculation. However, the number ofbreaths available for calculating the exponential asymptote is limited,and as a result, determination of the mixed-venous CO₂ is highlysensitive to errors in the end-tidal measurements.

Alternatively, in the method of Collier, the mixed-venous CO₂concentration is measured, but equilibration of the lung with themixed-venous CO₂ before recirculation depends on the initial volume andcomposition of the gas in the rebreathing bag. The optimal startingconditions vary with the subject's mixed-venous concentration of CO₂ andfunctional residual capacity so that, in practise, an effective startingvolume and concentration is determined by trial-and-error in repeatedexecutions of the rebreathing manoeuvre until a plateau is observed inthe end-tidal record [6].

In partial rebreathing methods, the last breath of the rebreathing phaseis assumed to represent the second steady state conditions required tocalculate the pulmonary blood flow. However, where the rebreathingperiod is short, equilibrium is not achieved; and, where the rebreathingperiod is long recirculation confounds the measurement [10].

Therefore, although measuring pulmonary blood flow (Q) should be anintegral part of clinical monitoring and physiological research, it isnot routinely implemented because of the invasiveness, cost, orinaccuracy of existing methods. To be of the greatest utility, apulmonary blood flow monitor must provide accurate, rapid, andrepeatable measurements over a broad range of physiological andpathological conditions.

SUMMARY OF THE INVENTION

We have developed a novel system for non-invasively measuring thepulmonary blood flow that implements an iterative respiratory algorithmand thereby overcomes the limitations of previous methods. The methodcan be adapted to an automated system for non-invasively measuringpulmonary blood flow that provides for reliable monitoring of pulmonaryblood flow in a wide range of subjects and environments. According toone aspect, the invention is directed to a method of controlling a gasdelivery apparatus to deliver a test gas (TG) for non-invasivelydetermining a subject's pulmonary blood flow comprising the steps of:

-   -   (a) Controlling at least one apparatus controllable variable to        test one or more test values for an iterated variable in an        iterative algorithm by:        -   A) providing an inspired concentration of a test gas that            achieves a test concentration of the test gas in the            subject's end tidal exhaled gas;        -   B) using a test value of an iterated variable in an            iterative algorithm to set the gas delivery apparatus to            deliver, for at least one series of inspiratory cycles, an            inspiratory gas comprising a test gas that is computed to            target the test concentration of the test gas based on a            test value of the iterated variable;        -   C) obtaining input comprising measurements of a measurable            vaiable for at least one series of inspiratory cycles,            optionally end tidal concentrations of test gas for            expiratory cycles corresponding to the at least one series            of inspiratory cycles;        -   D) using at least one measurement obtained in step C) as a            reference end tidal concentration value to generate at least            one of the following outputs:            -   (1) a test value satisfies the test criterion;            -   (2) a refined test value;            -   wherein the reference end tidal concentration is a                surrogate steady state value and is used to generate the                refined test value;    -   (b) If output (1) is not obtained, repeating step (a) as        necessary at least until output (1) is obtained; and    -   (c) If output (1) is obtained, outputting a value for pulmonary        blood flow which, based on the test criterion, sufficiently        represents a subject's true pulmonary blood flow.

As described below, obtaining steady state values for at least oneapparatus controllable variable and an end tidal concentration of testgas for or as part of the test is central to exploiting key testmathematical relationships that may be employed in the iterativealgorithm. The rate of flow of inspiratory gas into the breathingcircuit, when determinative of alveolar ventilation can be used tocompute a minute volume of expired test gas. A variety of othernon-invasive or invasive ways of obtaining these values are known. Thesevalues may conveniently be resting steady state values. Therefore, whileit is not necessary to employ the invention to obtain these values, theyare employed in the execution of the iterative algorithm or for thealgorithm. Hence, according to a preferred embodiment of the invention,initial steady state values are obtained within or for the iterativealgorithm. For convenience, this stage of gathering input of steadystate values for the iterative algorithm is referred to as the baselinephase.

According to another aspect, the invention is directed to a method fornon-invasively determining pulmonary blood flow comprising obtainingsteady state values for minute volume of expired test gas and end tidalconcentration of test gas and implementing steps (a) to (c) as definedabove, the method adapted to be implemented by a gas delivery apparatusas defined herein. The method can be executed rapidly and isnon-therapeutic in nature. The method may be carried out as apreliminary step to obtaining a diagnosis in which obtaining pulmonaryblood flow is useful for the ensuing diagnosis or forms part of abroader diagnostic work-up.

According to yet another aspect, the invention is directed to a gasdelivery system adapted to deliver a test gas (TG) for non-invasivelydetermining a subject's pulmonary blood flow comprising:

A gas delivery apparatus;

A control system for controlling the gas delivery apparatus based on aniterative algorithm including controlling at least one apparatuscontrollable variable to test one or more test values for an iteratedvariable, the control system comprising a computer, the gas deliverysystem including means for:

-   -   A) Obtaining input of steady state values sufficient for input        into the differential Fick equation, optionally minute volume of        expired test gas and an end tidal concentration of test gas;    -   B) Obtaining input of a test concentration of the test gas in        the subject's end tidal exhaled gas wherein the test        concentration of test gas is achieved by administration of a        test gas bolus;    -   C) Using a test value of the iterated variable in an iterative        algorithm to set a gas delivery apparatus to deliver, for at        least one series of inspiratory cycles, a test gas that is        computed to maintain the test concentration of the test gas;    -   D) Obtaining input comprising measurements of end tidal        concentrations of test gas for expiratory cycles corresponding        to the at least one series of inspiratory cycles;    -   E) using at least one measurement obtained in step D) as a        reference end tidal concentration value to generate at least one        of the following outputs:        -   (1) the test value satisfies the test criterion;        -   (2) a refined test value;    -   wherein the reference end tidal concentration is a surrogate        steady state value and is used to generate the refined test        value;    -   wherein the control system is adapted to iteratively test a        series of test values for the iterated variable based on the        following criteria:        -   If output (1) is not obtained, repeating step (B) to (E) as            necessary at least until output (1) is obtained; and        -   If output (1) is obtained, outputting a value for pulmonary            blood flow which, based on the test criterion, sufficiently            represents a subject's true pulmonary blood flow.

The computer, as broadly defined herein is understood to supply all thenecessary components that are not contained with the gas deliveryapparatus. Optionally, a separate CPU runs program code used to controla gas delivery apparatus comprising one or more conventional componentsof a gas blender. The gas delivery apparatus may be operativelyconnected to one or more gas analyzers including a gas analyzer for thetest gas. The gas delivery apparatus is optionally operativelyassociated with a pressure transducer as described below. The computerreceives inputs from one or more input devices for inputting values forvarious test parameters and values described herein and inputs from thegas analyzer and pressure transducer and provide outputs to suitableflow controllers and a computer readout for example a screen to outputof key parameters and values described herein, including preferably avalue for pulmonary blood flow.

The iterated variable is preferably pulmonary blood flow and optionallymay be an iterated variable determined by pulmonary blood flow fromwhich pulmonary blood flow may be calculated. For example, depending onthe choice of test gas, the iterated variable may be the mixed venousconcentration of the test gas.

The iterative algorithm is characterized in that it defines amathematical relationship between the at least one apparatuscontrollable variable, the iterated variable and a measurable variable,optionally the end tidal concentration attained by setting the apparatuscontrollable variable, such that the iterative algorithm isdeterminative of whether iteration on the test value satisfies a testcriterion.

The iterative algorithm preferably employs a test mathematicalrelationship based on the Fick equation and differential Fick equation.The iterative algorithm optionally employs equation 5 or 5-0.

The iterative algorithm may be based on the Fick or differential Fickequation.

The at least one apparatus controllable variable is optionally acontrollable inspired concentration of test gas in the inspiratory gas.

The at least one apparatus controllable variable is optionally acontrollable rate of flow of test gas-containing inspiratory gas intothe breathing circuit such that the rate of flow is indicative of ordeterminative of the alveolar ventilation, as described below.

The apparatus controllable variable may be both a selectable inspiredconcentration of test gas in the inspiratory gas and the rate of flow ofthe inspiratory gas into the breathing circuit For convenience, theapparatus controllable variable is preferably a selectable inspiredconcentration of test gas in the inspiratory gas which targets the testconcentration of test gas in the end tidal gas obviating the need tochange the rate of flow of inspiratory gas set for the test.

The iterative algorithm may in one embodiment rely on equation 5 or 5-0as the test mathematical relationship which is based on the Fickequation to solve for an the inspired concentration of test gas in theinspiratory gas which targets the test concentration of test gas in theend tidal gas. The equation may be equation 7a or 7a-0 as defined below.These equations pertain to CO₂ as a test gas but may be generalized toanother test gas. Inputs in equation 7a and 7a-0 may be obtained fromequations 6a and 6b, and 6a-0/6b-0, respectively, which may also begeneralized to another test gas where the relationship between end tidaland arterial values is established or readily ascertained.

The iterative algorithm may rely on equation 5 or 5-0 to solve for arate of flow of inspiratory gas into the breathing circuit which targetsthe test concentration of test gas in the end tidal gas. The equationmay be equation 7b or 7b-0 as defined below. These equations pertain toCO₂ as a test gas but may be generalized to another test gas where therelationship between end tidal and arterial values is established orreadily ascertained. Inputs in equation 7b and 7b-0 may be obtained fromequations 6a and 6b, and 6a-0/6b-0, respectively, which may also begeneralized to another test gas where the relationship between end tidaland arterial values is established or readily ascertained.

The at least one apparatus controllable variable is optionally the rateof flow of test gas-containing inspiratory gas into the breathingcircuit such that the rate of flow is determinative and reliablyindicative of the alveolar ventilation. For example, the alveolarventilation of a subject that is paralyzed and not making an independentinspiratory effort may be controlled by a ventilator setting.

Preferably the rate of flow of test gas-containing inspiratory gas intothe breathing circuit is determinative of the alveolar ventilation,optionally wherein the fresh gas flow is set to be equal to or less thanthe minute ventilation and the balance of the subject's inspiratoryrequirements are made up by a neutral gas, [11] for example re-breathedgas.

Optionally, the breathing circuit is a sequential gas delivery circuitwhich allows a subject to re-breath expired end tidal gas when the flowof gas into the breathing circuit is set to be equal to or less than theminute ventilation. The circuit may organize passive access to therebreathed gas. The flow of gas may be set to fill an inspiratoryreservoir which the subject can then deplete in each inspiratory cycle,whereupon negative pressure in the circuit triggers access to are-breathed gas until the end of inspiration.

Optionally, the refined test value is ascertained based on thedifferential Fick equation (eq. 3a1 or 3b1), by using steady statevalues of VCO2 and CaCO2, optionally resting steady state valuesobtained prior to establishing a test concentration of test gas in theend tidal gas. These values are important inputs into other equations aswell. In this manner, the reference end tidal concentration is used togenerate a refined test value for the iterated variable. Alternatively,the estimate can be refined based on an estimate obtained usingequations 3a2 or 3b2 as described below.

The “test concentration” of the test gas is the arterial concentrationof test gas following administration a test gas bolus as reflected inthe end tidal gas following the inspiratory cycle in which the test gasbolus is administered. A test gas bolus is one which achieves aphysiologically compatible test concentration of the test gas in thearterial circulation, and increases the concentration of the test gassufficiently to make the iterative testing of test values (one or moresuccessive test values) accurate having regard to the test criterion andthe speed/accuracy of the gas delivery apparatus and gas sensor used tomeasure the end tidal concentration values. Optionally, when using asequential gas delivery circuit to perform the test, a testconcentration of test gas may be administered by reducing theinspiratory flow in a manner (e.g. setting the flow to 0 for one breath)in which the test gas bolus is constituted by exhaled gas, for example,where the test gas is carbon dioxide a gas having a higher concentrationof carbon dioxide.

The test criterion optionally serves to define an acceptable differencebetween the reference end tidal concentration of test gas and the testconcentration of test gas, which establishes that a test value or arefined test value is acceptably close to a value from which the truepulmonary blood flow can be ascertained. The test criterion may also beto iterate a defined number of times. The test criterion may be tocontinue the iteration indefinitely by fixing this outcome (e.g. bydetermining that satisfaction of the test criterion is false).

Therefore, according to one embodiment, the invention is directed to amethod of controlling a gas delivery apparatus to deliver a test gas(TG) for non-invasively determining a subject's pulmonary blood flowcomprising the steps of:

-   -   (a) Controlling the flow of an inspiratory gas comprising a test        gas into a breathing circuit, wherein the concentration of the        test gas in the inspiratory gas (FiTG_(gl)) or the rate of flow        of gas into the circuit is adjusted to test one or more test        values for a iterated variable selected from the group        comprising pulmonary blood flow or mixed venous test gas        concentration (CvTG) by:        -   A) obtaining input of a steady state end tidal concentration            and at least one corresponding apparatus controllable            variable        -   B) providing an inspired concentration of a test gas that            achieves a test concentration of the test gas in the            subject's end tidal exhaled gas;        -   C) using a test value of an iterated variable in a test            mathematical relationship to set the gas delivery apparatus            to deliver, for at least one series of inspiratory cycles, a            test gas that is computed to maintain the test concentration            of the test gas;        -   D) obtaining input comprising measurements of end tidal            concentrations of test gas for expiratory cycles            corresponding to the at least one series of inspiratory            cycles;        -   E) using at least one measurement obtained in step D) as a            reference end tidal concentration value to generate at least            one of the following outputs:        -   (1) the test value satisfies the test criterion;        -   (2) a refined test value, wherein the reference end tidal            concentration is a surrogate steady state value and is used            to generate the refined test value;    -   (b) If output (a) is not obtained, repeating step (a) as        necessary until output (1) is obtained; and    -   (c) If output (1) is obtained, outputting a value for pulmonary        blood flow which, based on the test criterion, that sufficiently        represents a subject's true pulmonary blood flow.

Optionally, the reference end tidal concentration is the last end tidalconcentration value obtained prior to a recirculation or an average ofthe last end tidal concentration values.

According to another aspect, the invention is directed to a method fornon-invasively determining a subject's pulmonary blood flow comprisingthe steps of:

-   -   (a) Controlling the flow of an inspiratory gas comprising a test        gas into a breathing circuit, wherein the concentration of the        test gas in the inspiratory gas (FiTG_(gi)) or the rate of flow        of gas into the circuit is adjusted to test one or more test        values for a iterated variable selected from the group        comprising pulmonary blood flow or mixed venous test gas        concentration (CvTG) by:        -   A) obtaining input of a steady state end tidal concentration            and a corresponding value of at least one apparatus            controllable variable;        -   B) providing an inspired concentration of a test gas that            achieves s a test concentration of the test gas in the            subject's end tidal exhaled gas;        -   C) using a test value of an iterated variable in a test            mathematical relationship to set the gas delivery apparatus            to deliver, for at least one series of inspiratory cycles, a            test gas that is computed to maintain the test concentration            of the test gas;        -   D) obtaining input comprising measurements of end tidal            concentrations of test gas for expiratory cycles            corresponding to the at least one series of inspiratory            cycles;        -   E) using at least one measurement obtained in step C) as a            reference end tidal concentration value to generate at least            one of the following outputs:        -   (3) the test value satisfies the test criterion;        -   (4) a refined test value, wherein the reference end tidal            concentration is a surrogate steady state value and is used            to generate the refined test value;    -   (b) If output (a) is not obtained, repeating step (a) as        necessary until output (1) is obtained; and    -   (c) If output (1) is obtained, outputting a value for pulmonary        blood flow which, based on the test criterion, that sufficiently        represents a subject's true pulmonary blood flow.

According to optional embodiments of a method as defined above:

-   -   1. the test gas is carbon dioxide;    -   2. a subject's consumption of the test gas containing        inspiratory gas is controlled to define the subject's alveolar        ventilation (the minute volume of gas which reaches the alveoli        and may participate in gas exchange).    -   3. the subject's alveolar ventilation is defined by setting the        rate of flow of a test gas containing gas into a breathing        circuit to be equal to or less than the subject's minute        ventilation and delivering to the subject on inspiration, the        test gas containing inspiratory gas and when the test gas is        depleted for a breath, for the balance of that breath, a neutral        (for example re-breathed) gas.

According to another aspect the invention is directed to an inpiratorygas delivery system for non-invasively determining pulmonary blood flowcomprising:

-   -   (a) A gas delivery apparatus;    -   (b) A control system for controlling the gas delivery apparatus        including:        -   Means for obtaining input of:            -   a. a steady state value of an end tidal concentration of                a test gas and a corresponding value for at least one                apparatus controllable variable;            -   b. a test concentration of a test gas in the subject's                end tidal gas;            -   c. test value for an iterated variable for input into an                iterative algorithm;            -   d. a test criterion;            -   e. a reference end tidal concentration representing a                surrogate steady state value;        -   Means for computing:            -   f. a value for at least one apparatus controllable                variable, said value computed by the iterative algorithm                to maintain the test concentration of test gas in the                subject's end tidal gas for a series of inspiratory                cycles, the reference end tidal concentration selected                or computed from selected measurements of end tidal                concentrations of test gas for expiratory cycles                corresponding to the at least one series of inspiratory                cycles;            -   g. iteratively, where a previously computed test value                does not meet the test criterion, until a test criterion                is met, a refined test value for a iterated variable and                a corresponding value for an apparatus controllable                variable generated by the iterative algorithm for an                ensuing series of inspiratory cycles so as to provide a                new reference end tidal concentration for comparison to                the then current reference test concentration; and                -   means for outputting a test value for a iterated                    variable that meets the test criterion.

Suitable sequential gas delivery circuits and related apparatusinformation are disclosed WO/2004/073779, WO/2002/089888 andWO/2001/074433.

To compute the apparatus controlled variable required to maintain thetest gas concentration in the end-tidal exhaled gas, the followinginputs are needed: the test gas concentration in the end-tidal exhaledgas to be maintained, and a steady state end tidal test gasconcentration and a corresponding value of at least one apparatuscontrollable variable. To refine the estimate of the test value, thefollowing inputs are needed: a steady state end tidal test gasconcentration and a corresponding value of at least one apparatuscontrollable variable, and a reference end tidal test gas concentrationand a corresponding value of at least one apparatus controllablevariable.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic representation of one embodiment of a gas deliverysystem according to the invention.

FIG. 2 is a flowchart describing an iterative algorithm employed torecursively determine pulmonary blood flow according to a preferredembodiment of the invention.

FIG. 3 is a series of a graphical depictions of iterations of theiterative algorithm in which the effect on maintaining a testconcentration of test gas for different test values for pulmonary flowis depicted.

FIG. 4 is a graphical depiction of the effect of over-estimating,under-estimating and correctly estimating a test value for a testvariable, in this case, pulmonary blood flow.

DETAILED DESCRIPTION OF THE INVENTION

Table 1 (below) sets out a list of abbreviations used to express themathematical relationships employed in the description of severalembodiments of the invention described herein.

TABLE 1 SGD Sequential gas delivery G1 The gas being supplied to the SGDcircuit from a gas blender {dot over (V)}_(g1) The flow rate of G1 gasfrom the gas blender to the SGD circuit Alveolar The minute volume ofgas that reaches the alveoli and may contribute to gas ventilationexchange. Alveolar ventilation = {dot over (V)}_(g1) when SGD isimplemented. {dot over (V)}_(g1, R) The flow rate of G1 gas from the gasblender to the SGD circuit throughout the baseline phase {dot over(V)}_(g1, T) The flow rate of G1 gas from the gas blender to the SGDcircuit throughout the test phase FICO_(2, g1) Fractional concentrationof CO₂ in the G1 gas FIO_(2, g1) Fractional concentration of O₂ in theG1 gas FETCO₂ End-tidal fractional concentration of CO₂ FETO₂ End-tidalfractional concentration of O₂ CaCO₂ Concentration of CO₂ in thearterial blood CvCO₂ Concentration of CO₂ in the mixed-venous blood {dotover (Q)} Pulmonary blood flow {dot over (V)}CO₂ Minute volume ofexpired CO₂ FICO_(2, g1, R) Fractional concentration of CO₂ in the G1gas throughout the baseline phase FETCO_(2, R) End-tidal fractionalconcentration of CO₂ at the end of the baseline phase FETO_(2, R)Average end-tidal fractional concentration of O₂ during the baselinephase CaCO_(2, R) Concentration of CO₂ in the arterial blood at the endof the baseline phase {dot over (V)}CO_(2, R) Minute volume of expiredCO₂ at the end of baseline phase FICO_(2, g1, T) Fractionalconcentration of CO₂ in G1 gas throughout the test phase FETCO_(2, T)End-tidal fractional concentration of CO₂ at the end of the test phaseFETO_(2, T) Average end-tidal fractional concentration of O₂ during thetest phase CaCO_(2, T) Concentration of CO₂ in the arterial blood at theend of the test phase {dot over (V)}CO_(2, T) Minute volume of expiredCO₂ at the end of the test phase FICO_(2, g1, B) Fractionalconcentration of CO₂ in the G1 gas for the bolus breath FETCO_(2, B)End-tidal fractional concentration of CO₂ of the exhalation immediatelyafter inhalation of the bolus CaCO_(2, B) Concentration of CO₂ in thearterial blood immediately after inhalation of the bolus {dot over(Q)}_(est) An estimate of pulmonary blood flow used to try and clamp theend-tidal CO₂ during the test phase CvCO_(2, est) An estimate of theconcentration of CO₂ in the mixed-venous blood used to try and clamp theend-tidal CO₂ during the test phase {dot over (Q)}_(calc) The pulmonaryblood flow calculated at the end of the test phase CvCO_(2, calc) Theconcentration of CO₂ in the mixed-venous blood calculated at the end ofthe test phase {dot over (Q)}_(act) The subject's actual pulmonary bloodflow CvCO_(2, act) The subject's actual concentration of CO₂ in themixed-venous FRC Functional residual capacity RR Respiratory rate

Table 2 (below) lists the various mathematical relationships employed inthe description of embodiments of the invention described herein.

TABLE 2 Label Equation Description 1 {dot over (V)}CO₂ = {dot over(Q)}(CvCO₂ − CaCO₂) Fick equation which mathematically expresses thefact that if the end-tidal CO₂ is not changing, the minute volume (flux)of expired CO₂ is equal to the CO₂ deposited in the lung from thecirculation 2 {dot over (V)}CO′₂ = {dot over (Q)}(CvCO₂ − CaCO′₂) Fickequation showing that end- tidal and arterial CO₂ can be maintainedsteady at any level for a constant cardiac output and mixed-venousconcentration 3a1$\overset{.}{Q} = \frac{{\overset{.}{V}{\left( {CO} \right)^{\prime}}_{2}} - {\overset{.}{V}\left( {CO} \right)_{2}}}{{CaCO}_{2} - {{CaCO}^{\prime}}_{2}}$If two steady states of end-tidal CO₂ can be induced and measured for aconstant cardiac output and mixed-venous CO₂, (1) and (2) can be solvedsimultaneously for the cardiac output 3b1${C\overset{\_}{v}{CO}_{2}} = \frac{{{{CaCO}_{2} \cdot \overset{.}{V}}{{CO}^{\prime}}_{2}} - {{{{CaCO}^{\prime}}_{2} \cdot \overset{.}{V}}{CO}_{2}}}{{\overset{.}{V}{{CO}^{\prime}}_{2}} - {\overset{.}{V}{CO}_{2}}}$If two steady states of end-tidal CO₂ can be induced and measured for aconstant cardiac output and mixed-venous CO₂, (1) and (2) can be solvedsimultaneously for the mixed- venous CO₂ concentration 4${\overset{.}{V}{CO}_{2}} = {{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{\underset{BTPS}{\underset{}{293}}} \cdot \left\lbrack {{\underset{Haldane}{\underset{}{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,{g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right)}} \cdot {FETCO}_{2}} - {FICO}_{2,{g\; 1}}} \right\rbrack}$Calculation of the minute volume (flux) of expired CO2 from theend-tidal gases and the flow of gas to a sequential gas delivery circuit5${{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left\lbrack {{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,{g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right) \cdot {FETCO}_{2}} - {FICO}_{2,{g\; 1}}} \right\rbrack} = {\overset{.}{Q}\left( {{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}$Substitution of (4) for {dot over (V)}CO₂ in (1) 6a${C\overset{\_}{v}{CO}_{2}} = {\frac{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left\lbrack {{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,{g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right) \cdot {FETCO}_{2}} - {FICO}_{2,{g\; 1}}} \right\rbrack}{\overset{.}{Q}} + {CaCO}_{2}}$Rearrangement of (5) for the mixed-venous CO₂ where the end- tidalgases, the flow of gas to a sequential gas delivery circuit, thearterial CO₂ concentration, and cardiac output are known or estimated 6b$\overset{.}{Q} = \frac{\overset{.}{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left\lbrack {{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,{g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right) \cdot {FETCO}_{2}} - {FICO}_{2,{g\; 1}}} \right\rbrack}}{{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}}$Rearrangement of (5) for the cardiac output where the end-tidal gases,the flow of gas to a sequential gas delivery circuit, the arterial CO₂concentration, and the mixed-venous CO₂ concentration are known orestimated 7a${FICO}_{2,{g\; 1}} = \frac{{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot {FETCO}_{2} \cdot \left( {{FIO}_{2,{g\; 1}} - 1} \right)} + {{\overset{.}{Q}\left( {{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}\left( {1 - {FETO}_{2} - {FETCO}_{2}} \right)}}{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left( {{FETO}_{2} - 1} \right)}$Rearrangement of (5) for the inspired fraction of CO₂ required tomaintain end-tidal CO₂ at a steady state where the end-tidal gases, theflow of gas to a sequential gas delivery circuit, the arterial CO₂concentration, the mixed-venous CO₂ concentration, and cardiac outputare known or estimated 7b${\overset{.}{V}}_{g\; 1} = \frac{\overset{.}{Q}\left( {{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}{\frac{310}{293} \cdot \left\lbrack {{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,{g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right) \cdot {FETCO}_{2}} - {FICO}_{2,{g\; 1}}} \right\rbrack}$Rearrangement of (5) for the G1 gas flow required to maintain end- tidalCO₂ at a steady state where the end-tidal gases, the fractionalconcentration of CO₂ in the G1 gas, the arterial CO₂ concentration, themixed-venous CO₂ concentration, and cardiac output are known orestimated 8${FICO}_{2,{g\; 1},B} = \frac{{RR} \cdot \left\lbrack {{\left( {{FETCO}_{2,R} + \frac{10}{{PB} - 47}} \right)\left( {{FRC} + \frac{{\overset{.}{V}}_{g\; 1}}{RR}} \right)} - {{FRC} \cdot {FETCO}_{2,R}}} \right\rbrack}{{\overset{.}{V}}_{g\; 1}}$Can be used to estimate the fractional concentration of CO₂ required inthe bolus breath to raise end-tidal CO₂ by about 10 mmHg from baseline 9|FETCO_(2, T, x) − FETCO_(2, T, x−1)|< |FETCO_(2, T, x+1) −FETCO_(2, T, x)| Applied to each breath of the test to detectrecirculation of the arterial blood 3a2 {dot over (Q)}_(calc) = {dotover (Q)}_(est) + k(FETCO_(2, B) − FETCO_(2, T)) k > 0 An alternative tocalculate cardiac output from an estimated cardiac output and the driftof end-tidal CO₂ observed during a test executed with said estimate 3b2CvCO_(2, calc) = CvCO_(2, est) − k(FETCO_(2, B) − FETCO_(2, T)) k > 0 Analternative to calculate mixed- venous CO₂ from an estimatedmixed-venous CO₂ and the drift of end-tidal CO₂ observed during a testexecuted with said estimate 4-O${\overset{.}{V}{CO}_{2}} = {{\overset{.}{V}}_{g\; 1} \cdot \underset{BTPS}{\frac{310}{\underset{}{293}}} \cdot \left\lbrack {{FETCO}_{2} - {FICO}_{2,{g\; 1}}} \right\rbrack}$An alternative, slightly less accurate, measure of minute volume ofexpired CO₂ than (4) when oxygen monitoring is not present. 5-O${{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left\lbrack {{FETCO}_{2} - {FICO}_{{2,{g\; 1}}\;}} \right\rbrack} = {\overset{.}{Q}\left( {{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}$Substitution of (4-O) for {dot over (V)}CO₂ in (1) 6-O${C\overset{\_}{v}{CO}_{2}} = {\frac{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left\lbrack {{FETCO}_{2} - {FICO}_{2,{g\; 1}}} \right\rbrack}{\overset{.}{Q}} + {CaCO}_{2}}$Rearrangement of (5-O) for the mixed-venous CO₂ where the end- tidalCO₂, the flow of gas to a sequential gas delivery circuit, the arterialCO₂ concentration, and cardiac output are known or estimated 6b-O$\overset{.}{Q} = \frac{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left\lbrack {{FETCO}_{2} - {FICO}_{2,{g\; 1}}} \right\rbrack}{{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}}$Rearrangement of (5-O) for the cardiac output where the end-tidal CO₂,the flow of gas to a sequential gas delivery circuit, the arterial CO₂concentration, and the mixed-venous CO₂ concentration are known orestimated 7a-O${FICO}_{2,{g\; 1}} = {{FETCO}_{2} - \frac{\overset{.}{Q}\left( {{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293}}}$Rearrangement of (5-O) for the inspired fraction of CO₂ required tomaintain end-tidal CO₂ at a steady state where the end-tidal CO₂, theflow of gas to a sequential gas delivery circuit, the arterial CO₂concentration, the mixed-venous CO₂ concentration, and cardiac outputare known or estimated 7b-O${\overset{.}{V}}_{g\; 1} = \frac{\overset{.}{Q}\left( {{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}{\frac{310}{293} \cdot \left\lbrack {{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,{g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right) \cdot {FETCO}_{2}} - {FICO}_{2,{g\; 1}}} \right\rbrack}$Rearrangement of (5-O) for the G1 gas flow required to maintainend-tidal CO₂ at a steady state where the end-tidal CO₂, the fractionalconcentration of CO₂ in the G1 gas, the arterial CO₂ concentration, themixed-venous CO₂ concentration, and cardiac output are known orestimated

The term “reference end tidal concentration” is used to describe a valueobtained by measurement which reflects an arterial blood concentrationof the test gas preferably obtained prior to a recirculation time,preferably a value or one or more averaged values obtained closest intime to recirculation since this value may most usefully reflect a newsteady state value achieved as a result of administering the test gas.In this connection, it is noteworthy that although the differential Fickequation is a steady state equation, using reference end tidal test gasconcentrations obtained before a steady is reached does not prevent theadjusted test value for the iterated variable to be refined recursively.Therefore, the “reference end tidal concentration” is preferably atleast a “surrogate steady state value” i.e. a value preferably obtainedbefore a recirculation time that equals or sufficiently represents asteady state value to make the iterative process of meeting the testcriterion useful in practice. To reduce the number of iterationsrequired to determine pulmonary blood flow, the surrogate steady statevalue is preferably selected to be one value, or one or more averagedvalues, determined to be closest to a recirculation time—generally oneor more among the last test values obtained prior to a recirculation.Equation 9 may be used at each breath to detect recirculation of thearterial blood.

The term “refined test value” is used to refer to a value for a iteratedvariable that is revised relative a previous test value. Since theinvention contemplates that more than one iterated variable may beemployed and since the iterated variables are mathematicallyinterrelated the term refined test value should be understood to includea value indirectly derived from data related to a prior test valuerelated to another iterated variable.

The reference to an iterated variable which is determined by pulmonaryblood flow and from which pulmonary blood flow can be computed generallyrefers to a mixed venous test gas concentration. In contrast to carbondioxide, with respect to test gases such as oxyacetylene, which are notproduced or reliably consumed, the mixed venous blood concentration isequal to the arterial concentration at steady state and hence may notprovide useful information about the pulmonary blood flow. In this case,the choice of iterated variable for iteration of a test value would bepulmonary blood flow. If pulmonary shunt is known total pulmonary bloodflow can also be used to compute total cardiac output.

The term “gas delivery apparatus” means a device that can be controlledto control the rate of flow of the test gas into the circuit or set theconcentration of the test gas into the inspiratory gas, and preferablyboth, for example a respiratory gas blender known to those skilled inthe art, for example a gas blender with rapid flow controllers,optionally a gas blender capable of delivering accurate mixes of threegases into the circuit. The apparatus and gas mixes may of the typedescribed in published WO 2007/02197. The key functionality of theapparatus is understood to serve the role of establishing (byadministering test gas containing inspiratory gas) and maintaining atest concentration of test gas. The gas delivery apparatus may beoperatively associated with suitable gas analyzers to measure fractionalcarbon dioxide and oxygen concentrations at the mouth. The apparatus isoperatively associated with a control system for controlling the gasdelivery apparatus. The control system demands the required output ofthe gas delivery apparatus to maintain a test concentration of test gasin the manner described above. The control system or the apparatuscomprises the necessary controllers for this purpose as described above,for example for controlling rate of flow of inspiratory gas andoptionally separate flow controllers for controlling the rate of flow ofthe sources gases.

The gas delivery apparatus comprises at least one input port forreceiving a source which may be an inspiratory gas containing the testgas, at least one output port for connection to a breathing circuit anda flow controller for controlling the rate of flow of the inspiratorygas.

The flow controller optionally controls a gas delivery means.

The term “gas delivery means”, abbreviated refers to specifically tohardware for delivering (e.g. releasing, where the source gas is underpressure) specific volumes of a source gas comprising or consisting ofthe test gas for inspiration by the patient, preferably a device that isadapted to output volumes of variable incremental size. The gas deliverymeans may be any known gas delivery device such as a gas injector, or avalve, for example, a proportional flow control valve.

Optionally, the gas delivery apparatus is a gas blender, for example, anapparatus that comprises a plurality of input ports for connection to aplurality of gas sources in order to blend different gases that make upthe test gas containing gas, for example oxygen, air, nitrogen and atest gas. Optionally, carbon dioxide is the test gas. A flow controlleroptionally controls a proportional solenoid valve operatively associatedwith each gas source and optionally a separate flow controller and valveis employed to set the rate of flow of the blended gas into a breathingcircuit. Input devices are used to set the rate of flow of gas into thebreathing circuit and the concentration of the test gas in the gasprovided to the subject.

According to one aspect the invention is directed to a computer programproduct which implements a method according to the invention. Thecomputer program product comprises a non-transitory computer readablemedium encoded with program code for controlling operation of gasdelivery device, the program code including code for iterativelygenerating a series of test values of a iterated variable based on aniterative algorithm as described above in order to maintain a testconcentration of test gas. The program code may comprise code for:

-   -   A) providing an inspired concentration of a test gas that        defines a test concentration of the test gas in the subject's        end tidal exhaled gas;    -   B) using an iterative algorithm to set the gas delivery        apparatus to deliver, for at least one series of inspiratory        cycles, a test gas that is computed to target the test        concentration of the test gas based a test value of the iterated        variable;    -   C) obtaining input comprising measurements of end tidal        concentrations of test gas for expiratory cycles corresponding        to the at least one series of inspiratory cycles;    -   D) using at least one measurement obtained in step C) as a        reference end tidal concentration value to generate at least one        of the following outputs:    -   (1) the test value satisfies the test criterion;    -   (2) a refined test value;    -   wherein the reference end tidal concentration is a surrogate        steady state value and the refined test value is ascertainable        from the reference end tidal concentration;

The program code may include code to test a series of test values forthe iterated variable based on the following criteria:

-   -   If output (1) is not obtained, repeating step (A) to (D) as        necessary at least until output (1) is obtained; and    -   If output (1) is obtained, outputting a value for pulmonary        blood flow which, based on the test criterion, sufficiently        represents a subject's true pulmonary blood flow.

As described above, the computer readable medium or computer readablememory has recorded thereon computer executable instructions forcarrying out one or more embodiments of the above-identified methods.The invention is not limited by a particular physical memory format onwhich such instructions are recorded for access by a computer.Non-volatile memory exists in a number of physical forms includingnon-erasable and erasable types. Hard drives, DVDs/CDs and various typesof flash memory may be mentioned. The invention, in one broad aspect, isdirected to a non-transitory computer readable medium comprisingcomputer executable instructions for carrying out one or moreembodiments of the above-identified method.

The term “test concentration” means a concentration of a test gas in asubject's arterial blood as reflected in the end tidal concentration ofthe test gas in the subject's exhaled gas after attaining equilibriumwith that arterial concentration of test gas. As described above, thisconcentration is optionally achieved by arranging for a subject toobtain an inspiratory gas with any suitable concentration of test gaswhich may be delivered via the gas delivery apparatus or optionallyindirectly from a re-breathed gas.

The term “computer” is used broadly to refer to any device (constitutedby one or any suitable combination of components) which may used inconjunction with discrete electronic components to perform the functionscontemplated herein, including computing and obtaining input signals andproviding output signals, and optionally storing data for computation,for example inputs/outputs to and from electronic components andapplication specific device components as contemplated herein. Thecomputer may use machine readable instructions or dedicated circuits toperform the functions contemplated herein including without limitationby way of digital and/or analog signal processing capabilities, forexample a CPU, for example a dedicated microprocessor embodied in an ICchip which may be integrated with other components, for example in theform of a microcontroller. Key inputs may include input signals from agas analyzer, any type of input device for inputting inputs ascontemplate herein (for example, a knob, dial, keyboard, keypad, mouse,touch screen etc.) input from a computer readable memory etc. Keyoutputs include output of a control signal to control to a gas deliverymean such as a proportional control valve, for example outputs to a flowcontroller for controlling key components of gas delivery apparatus.

It is to be understood that an iterative algorithm may executecomputation based on a test mathematical relationship herein and thatthis relationships may be variously defined with equivalent formula inwhich terms/parameters are substituted by equivalent expressions thatare expressed in other forms or styles e.g. read from a graph etc.

Hence the invention is not limited by a reference to particularexpressions of a test mathematical relationship or related equations.For example, equation 5 may expressed by equivalent expressions ofequation 1 from which it is derived may be obtained by computing {dotover (V)}CO₂ (eq. 4) in a manner other than expressed in equation 4. Itis understood that the equations relate back to the Fick equation anddifferential Fick equation and hence a iterative algorithm expressed asbeing “based on” the Fick equation” is understood to be encompassequivalent expressions or expansions of the equation with and withoutcorrection factors. In contrast to prior methods, in one embodiment of amethod according to the invention, which is also primarily describedhereafter in connection with using carbon dioxide as an embodiment of a“test gas”, the invention contemplates obtaining steady state valuesoptionally when the subject is at “rest” and those values arestabilized. VCO₂ and CaCO₂ are measured in a first steady state. Ratherthan waiting for end-tidal CO₂ to exponentially drift up to some secondsteady-value (which notably is generally not achieved before arecirculation), the present method contemplates giving a bolus of CO₂ tomore acutely increase end-tidal CO₂ and calculate the inspired CO₂required to force a second steady state at the elevated end-tidal CO₂from a guess at the cardiac output. If the end-tidal CO₂ remains stable,the guess at cardiac output was correct. If the guess at cardiac outputwas incorrect, much like in the previous art, the end-tidal CO₂ willexponentially drift towards a steady state until recirculation. If weapply the differential Fick formula to our rest state and a second staterepresented for example by the last test breath before recirculation, itis possible to calculate a value for cardiac output. Much like previousmethods, if the last test breath doesn't actually represent steady state(i.e. equilibration did not occur before recirculation), the cardiacoutput calculated by the differential Fick will be in error. However, itwill be closer to the actual cardiac output than an original guess goingin, and therefore, represents a refined estimate of the actual cardiacoutput. If this procedure is executed again, but with the refinedestimate of cardiac output calculated from the last iteration, thenthere will be less drift during the test, the last test breath willbetter represent steady state, and again, our calculation of cardiacoutput will be even closer to the actual cardiac output. Repeat asnecessary and the cardiac output calculated by this method will convergeto the actual cardiac output. Accordingly, in contrast to prior methodsthere is no need to fit exponentials and extrapolate. In one embodiment,with sequential gas delivery (SGD), it is possible to clamp alveolarventilation, and therefore measure a very consistent VCO₂ with equation4 obviating the need for simultaneous flow/CO₂ measurements. Toimplement the test, an operator can provide a precise reduction inalveolar ventilation that will not be affected by changes in minuteventilation, and can therefore be used in spontaneous breathers andmechanically ventilated subjects.

Iterative NICO Equations

A method according to the invention will now be described in accordancewith a preferred embodiment of the invention in which the test gas iscarbon dioxide.

With the use of sequential gas delivery, alveolar ventilation can becontrolled independent of overall minute ventilation. As a result,EQUATION 4 provides an accurate measure of the net minute volume ofexpired CO₂ calculated from the end-tidal fractional concentrations ofCO₂ and O₂ (FETCO₂,FETO₂) without the use of breath collection orflowmetry.

EQUATION  4${\overset{.}{V}{CO}_{2}} = {{\overset{.}{V}}_{g\; 1} \cdot \underset{\underset{BTPS}{}}{\frac{310}{293}} \cdot \left\lbrack {{\underset{\underset{Haldane}{}}{\left( \frac{1 - {{FI}{CO}}_{2,{g\; 1}} - {{FI}O}_{2,{g\; 1}}}{1 - {{FET}{CO}}_{2} - {{FET}O}_{2}} \right)} \cdot {{FET}{CO}}_{2}} - {{FI}{CO}}_{2,{g\; 1}}} \right\rbrack}$

The correction term, BTPS, accounts for the expansion of gases in thelung owing to the increase in temperature from standard conditions. TheHaldane term applies the Haldane transform to calculate the expiredvolume when only the inspired volume is known.

When the amount of CO₂ in the alveolar space is unchanging, EQUATION 4can be substituted into EQUATION 1. The resulting steady state massbalance equation for the alveolar space is shown in EQUATION 5.

EQUATION  5${{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left\lbrack {{\left( \frac{1 - {{FI}{CO}}_{2,{g\; 1}} - {{FI}O}_{2,{g\; 1}}}{1 - {{FET}{CO}}_{2} - {{FET}O}_{2}} \right) \cdot {{FET}{CO}}_{2}} - {{FI}{CO}}_{2,{g\; 1}}} \right\rbrack} = {\overset{.}{Q}\left( {{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}$

Equation 5, based on the differential Fick equation, is a key testmathematical relationship from which other mathematical relationshipsare derived by solving for a test variable or an apparatus controllablevariable.

The results of solving EQUATION 5 for the mixed-venous concentration ofCO₂ and the pulmonary blood flow are shown in EQUATIONS 6.

                                   EQUATION  6a${C\overset{\_}{v}{CO}_{2}} = {\frac{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left\lbrack {{\left( \frac{1 - {{FI}{CO}}_{2,{g\; 1}} - {{FI}O}_{2,{g\; 1}}}{1 - {{FET}{CO}}_{2} - {{FET}O}_{2}} \right) \cdot {{FET}{CO}}_{2}} - {{FI}{CO}}_{2,{g\; 1}}} \right\rbrack}{\overset{.}{Q}} + {CaCO}_{2}}$                                   EQUATION  6b$\overset{.}{Q} = \frac{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left\lbrack {{\left( \frac{1 - {{FI}{CO}}_{2,{g\; 1}} - {{FI}O}_{2,{g\; 1}}}{1 - {{FET}{CO}}_{2} - {{FET}O}_{2}} \right) \cdot {{FET}{CO}}_{2}} - {{FI}{CO}}_{2,{g\; 1}}} \right\rbrack}{{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}}$

Similarly, the results of solving EQUATION 5 for the fractionalconcentration of CO₂ in the G1 gas and the flow rate of G1 gas are shownin EQUATIONS 7.

                                   EQUATION  7a${{FI}{CO}}_{2,{g\; 1}} = \frac{\begin{matrix}{{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot {{FET}{CO}}_{2} \cdot \left( {{{FI}O}_{2,{g\; 1}} - 1} \right)} +} \\{{\overset{.}{Q}\left( {{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}\left( {1 - {{FET}O}_{2} - {{FET}{CO}}_{2}} \right)}\end{matrix}}{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left( {{{FET}O}_{2} - 1} \right)}$                                   EQUATION  7b${\overset{.}{V}}_{g\; 1} = \frac{\overset{.}{Q}\left( {{C\overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}{\frac{310}{293} \cdot \left\lbrack {{\left( \frac{1 - {{FI}{CO}}_{2,{g\; 1}} - {{FI}O}_{2,{g\; 1}}}{1 - {{FET}{CO}}_{2} - {{FET}O}_{2}} \right) \cdot {{FET}{CO}}_{2}} - {{FI}{CO}}_{2,{g\; 1}}} \right\rbrack}$

The Iterative NICO Method

The partial pressure of CO₂ in the arterial blood is assumed to be equalto the end-tidal partial pressure of CO₂ and then converted to aconcentration via the CO₂ dissociation curve of oxygenated whole blood[3,4]. This requires haemoglobin concentration ([HB]). [HB] ispreferably obtained from a blood gas analysis. If blood gas analysis isnot possible, [HB] can be measured transcutaneously. Alternatively, [HB]can be obtained from the normal published ranges for age/sex. End-tidalfractional concentrations can be converted to partial pressures bymultiplying the fractional concentrations by barometric pressure (PB)less the partial pressure of water vapour.

The amount of CO₂ in the lung is entirely determined by the alveolarventilation and the diffusion of CO₂ between the circulation and thealveolar space. If the pulmonary blood flow or the mixed-venousconcentration of CO₂ is known, the other can be calculated from thesteady state minute volume of expired CO₂ and arterial CO₂ concentration(EQUATIONS 6a,b). Therefore, the transfer rate of CO₂ between thecirculation and the alveolar space can be determined for any value ofend-tidal CO₂ as long as the pulmonary blood flow and mixed-venousconcentration of CO₂ remains unchanged. Correspondingly, following anacute change in end-tidal CO₂ from a previously steady value, if thealveolar ventilation can be controlled or measured, a temporary steadystate at the new end-tidal CO₂ (referred to as a test concentration) canbe maintained by delivering the inspired fraction of CO₂ and/or alveolarventilation required to exactly offset the influx from the circulation(EQUATIONS 7). This steady state can be maintained until themixed-venous CO₂ changes due to recirculation of the affected arterialblood.

Our algorithm recursively exploits this observation to measure thepulmonary blood flow. According to one embodiment, throughout eachiteration, the alveolar ventilation (={dot over (V)}_(gl)) is set with asequential gas delivery circuit. The fraction of O₂ in the G1 gas(FIO_(2,gl)) is not important, but should be held constant at a levelsufficient to maintain arterial oxygen saturation. The end-tidal gasesare measured by continuous real-time analysis of the expired gas.

In the baseline phase, the fractional concentration of CO₂ in the G1 gas(FICO_(2,gl,R)) is set and held constant. Although not necessary,FICO_(2,gl,R) is usually zero. The G1 gas flow during the rest phase({dot over (V)}_(gl,R)) is usually set to about 80% of the subjectstotal measured or estimated minute ventilation. In general, {dot over(V)}_(gl,R) should be low enough to permit rebreathing which at leastfills the subject's anatomical dead space, but high enough to preventhypercapnia. The baseline phase can be ended when end-tidal CO₂ isstable. Stability of end-tidal CO₂ can be determined by thestandard-deviation of end-tidal CO₂ measured over five breaths beingwithin ±2 mmHg, or if the difference between the largest and smallestend-tidal CO₂ measured over the last 5 breaths is within ±2 mmHg, or ifthe slope of the linear regression line passing through the end-tidalCO₂ of the last five breaths is less than ±0.5 mmHg/breath.Alternatively, the baseline period can be ended after predefined timehas elapsed and/or predefined number of breaths has occurred.

At the end of the baseline phase, the end-tidal CO₂ during the baselinephase (FETCO_(2,R)) is converted to an arterial concentration (CaCO₂).The end-tidal CO₂ from the last breath of the baseline phase can be usedas FETCO_(2,R). Alternatively, FETCO_(2,R) can be the average of anumber of breaths at the end of the baseline phase. The baseline minutevolume of expired CO₂ ({dot over (V)}CO_(2,R)) is calculated fromEQUATION 4, using the average end-tidal O₂ (FETO_(2,R)) measured duringthe baseline phase, {dot over (V)}_(gl,R), FICO_(2,gl,R), FIO_(2,gl),and FETCO_(2,R). A test value for an iterated variable, e.g.mixed-venous concentration of CO₂ is estimated from EQUATION 6a using anestimate of the pulmonary blood flow ({dot over (Q)}_(est)), {dot over(V)}_(gl,R), FICO_(2,gl,R), FIO_(2,gl), FETCO_(2,R), FETO_(2,R), andCaCO_(2,R). Alternatively, a test value for pulmonary blood flow (apreferred iterated variable for convenience) is estimated starting froman estimate of the mixed-venous concentration of CO₂ (CvCO_(2,est))using EQUATION 6b with {dot over (V)}_(gl,R), FICO_(2,gl,R), FIO_(2,gl),FETCO_(2,R), FETO_(2,R), and CaCO_(2,R).

To transition from the baseline phase to the test phase, the inspiredfraction of CO₂ in the G1 gas is increased substantially for one bolusbreath, inducing a sharp increase in the end-tidal CO₂. The bolus breathmay optimally increase end-tidal CO₂ by approximately 10 mmHg to providesufficient measurement resolution and minimize discomfort to thepatient. The inspired fraction of CO₂ in the bolus breath(FICO_(2,gl,B)) required to elevate end-tidal CO₂ by approximately 10mmHg can be calculated using an approximation of the subject'sfunctional residual capacity (FRC), respiratory rate (RR), {dot over(V)}_(gl,R), and FETCO_(2,R) using EQUATION 8. The FRC can be estimatedor obtained from normal published ranges for the age, weight, and sex ofthe subject. Respiratory rate can be measured or estimated. For mostadults, FICO_(2,gl,B) of 15-20% should provide an adequate increase inend-tidal CO₂.

EQUATION  8${{FI}{CO}}_{2,{g\; 1},B} = \frac{{RR} \cdot \left\lbrack {{\left( {{{FET}{CO}}_{2,R} + \frac{10}{{PB} - 47}} \right)\left( {{FRC} + \frac{{\overset{.}{V}}_{g\; 1}}{RR}} \right)} - {{FRC} \cdot {{FET}{CO}}_{2,R}}} \right\rbrack}{{\overset{.}{V}}_{{g\; 1},R}}$

The elevated end-tidal CO₂ (FETCO₂), and corresponding arterial CO₂(CaCO_(2,B)) measured in the exhalation immediately followinginspiration of the bolus are recorded. This recorded value representsthe test concentration of CO2 sought to be maintained in the test phase.Subsequently, a value for an apparatus controllable variable preferablyselected from the inspired fraction of CO₂ (FICO_(2,gl,T)) and G1 flowrate ({dot over (V)}_(gl,T)) during the test phase are set to try andmaintain end-tidal CO₂ at FETCO_(2,B)·{dot over (V)}_(gl,T) can bechosen arbitrarily, but in general, {dot over (V)}_(gl,T) should be lowenough to permit rebreathing which at least fills the subject'sanatomical dead space. A test mathematical relationship solving forFICO2,gl (EQUATION 7a), with {dot over (Q)}_(est), CvCO_(2,est), {dotover (V)}_(gl,T), FIO_(2,gl), FETCO_(2,B), FETO_(2,R), and CaCO_(2,B),can be used to calculate FICO_(2,gl,T) presumed to force a second steadystate of end-tidal CO₂ at FETCO_(2,B). Alternatively, FICO_(2,gl,T) canbe set arbitrarily within the limitations of the hardware and the testmathematical relationship solves for Vg1 (EQUATION 7b), with {dot over(Q)}, CvCO_(2,est), FICO_(2,gl,T), FIO_(2,gl), FETCO_(2,B), FETO_(2,R),and CaCO_(B), can be used to calculate {dot over (V)}_(gl,T) presumed toforce a second steady state of end-tidal CO₂ at FETCO_(2,B). This {dotover (V)}_(gl,T) and FICO_(2,gl,T) is delivered until recirculation isdetected (described later), or for a predefined length of time presumedto be less than the recirculation time, or a predefined number ofbreaths presumed to occur before recirculation.

At the end of the test phase, the end-tidal CO₂ during the test phase(FETCO_(2,T)) is converted to an arterial concentration (CaCO_(2,T)).The end-tidal CO₂ from the last breath of the test phase can be used asa reference end tidal concentration (FETCO2,T). Alternatively,FETCO_(2,T) can be the average of values obtained for a number ofbreaths at the end of the test phase. The minute volume of expired CO₂during the test phase ({dot over (V)}CO_(2,T)) is calculated fromEQUATION 4, using the average end-tidal O₂ (FETO_(2,T)) measured duringthe test phase, {dot over (V)}_(gl,T), FICO_(2,gl,T), FIO_(2,gl), andFETCO_(2,T). Refined test values for pulmonary blood flow andmixed-venous CO₂ are recalculated ({dot over (Q)}_(calc),CvCO_(2,calc))from EQUATIONS 3a1,b1 using {dot over (V)}CO_(2,R), CaCO_(2,R), {dotover (V)}CO_(2,T), and CaCO_(2,T) or EQUATIONS 3a2,b2 using {dot over(Q)}_(est), CvCO_(2,est), FETCO_(2,B), and FETCO_(2,T). Subsequently,the system is returned to the baseline state.

This manoeuvre is repeated within successively refined test values forthe test variable utilizing either the calculated pulmonary blood flowof each test as the estimated pulmonary blood flow in the nextiteration, or the calculated mixed-venous CO₂ concentration as theestimated mixed-venous CO₂ concentration in the next iteration.

Selecting the Apparatus Controllable Variable and its Values:

Although {dot over (V)}_(gl,R) can be chosen arbitrarily, in general,{dot over (V)}_(gl,R) should be low enough to permit rebreathing whichat least fills the subject's anatomical dead space, but high enough toprevent hypercapnia. Although FICO_(2,gl,R) can be chosen arbitrarily,in general, there is not often a reason to deliver CO₂ in the baselinephase, and FICO_(2,gl,R) is generally set to zero. Although either {dotover (V)}_(gl,T) or FICO_(2,gl,T) can be set arbitrarily and the othervalue for the apparatus controllable variable calculated from EQUATIONS7a,b, it is simplest to set {dot over (V)}_(gl,T) equal to {dot over(V)}_(gl,R) during the test phase and calculate FICO_(2,gl,T) fromEQUATION 7a.

No O₂

It is pertinent to note that knowledge of inspired and end-tidal O₂ isonly required to implement the Haldane transform (EQUATION 4) whichgives a measure of expired volumes when only inspired volumes are known.In practise, the expired volumes are not significantly different thaninspired volumes. Where an oxygen analyzer is not present, the iterativealgorithm method described herein can be executed with a small loss inaccuracy using equations ending with (—O). (e.g. 7a-0, 7b-0, etc.)

Initiation and Convergence and Termination

The initial test value for the iterated variable, be it pulmonary bloodflow or mixed-venous CO₂, is taken as the middle of the normal publishedrange for the age, height, weight, and sex of the subject.Alternatively, the initial pulmonary blood flow or mixed-venous CO₂estimate can be arbitrary. Alternatively, the test value for pulmonaryblood flow can be estimated as 0.07 L/min/kg of subject body weight.Alternatively, the initial pulmonary blood flow or mixed-venous CO₂estimate can be obtained from a pervious execution of the recursivealgorithm. Alternatively, the initial test value for pulmonary bloodflow or mixed-venous CO₂ can be obtained from another measurementtechnique (thermodilution, mixed-venous blood gases). Alternatively, themixed-venous partial pressure of CO₂ can be estimated as 6 mmHg abovethe resting end-tidal CO₂ and converted to a concentration via the CO₂dissociation curve.

If the test value for pulmonary blood flow does not satisfy the testcriterion, the predicted transfer rate of CO₂ between the circulationand the alveolar space will also be in error. However, the minute volumeof expired of CO₂ in the test phase will exponentially equilibrate withthe flux across the blood-alveolar interface. As a result, the pulmonaryblood flow calculated in each test will be refined and better reflectthe actual pulmonary blood flow ({dot over (Q)}_(act)) than the ingoingtest value. Because the iterative algorithm is implemented recursively,and the estimated test value for the iterative variable is refined aftereach iteration to reflect the previously calculated test values, thealgorithm converges to the actual physiological parameters of thesubject.

The rate at which the calculated parameters converge to the actualparameters depends on how fast the end-tidal CO₂ approaches equilibriumin the test phase. The derivative of an exponential function is largestat the start and vanishes with time. Therefore, a substantial refinementin the estimated parameters occurs in the breaths before recirculation.As a result, the calculated parameters at the end of each test aresignificantly more accurate than the previous estimates.

Testing is optionally terminated when the difference in pulmonary bloodflow calculated between subsequent tests differs in magnitude less thana user-definable threshold. Optionally, the algorithm can be continuedindefinitely. Optionally, the algorithm can be executed for a predefinednumber of iterations. All of these options satisfy a test criterion.

Detection of Recirculation

The pulmonary recirculation time varies between individuals, and withinthe same individual in different hemodynamic states. Indeed, thereported interval before recirculation occurs differs significantlyamongst investigators.

We detect the occurrence of recirculation by analysis of the time courseof the end-tidal CO₂ during the test phase. Prior to recirculation, theend-tidal CO₂ approaches a steady value exponentially—the absolutedifference between consecutive end-tidal measurements decreases as thetest proceeds. Recirculation causes a deviation from this asymptoticapproach, detectable as an increase in the difference betweenconsecutive end-tidal CO₂ measurements. Accordingly, in our method, thetest proceeds as long as the magnitude of the difference betweenconsecutive end-tidal CO₂ measurements is decreasing.

More specifically, let FETCO_(2,T,x) be the end-tidal CO₂ of a breathduring the test phase, and FETCO_(2,T,x−1) and FETCO_(2,T,x+1) be thebreaths immediate before and after.

The last breath before recirculation is the first test breath for which:

|FETCO_(2,T,x)−FETCO_(2,T,x−1)|<|FETCO_(2,T,x+1)−FETCO_(2,T,x)|  EQUATION9

Apparatus

According to one embodiment of a gas delivery system, the systemapparatus is shown in FIG. 1. It consists of a gas blender 22, asequential gas delivery circuit 26, gas analyzers for oxygen 16 andcarbon dioxide 18, a pressure transducer 14, a computer 8 includingsoftware 10 (which is optionally embodied a computer program product)that works the gas blender 22 to request gas flows and with the gasanalyzers 16 and 18, pressure transducer 14 and input devices formeasured or estimated physiological parameters 36 and algorithm settings34 to obtain inputs as contemplated herein. The gas blender 22 may beconnected to three pressurized gas tanks 32. The gas blender optionallycontains three rapid flow controllers (not shown) capable of deliveringaccurate mixes of three source gases, optionally comprised of CO₂, O₂,and N₂ to the circuit. The concentrations of CO₂, O₂, and N₂ in thesource gases must be such that they can produce the blends required tocarry out the algorithm. Pure CO₂, O₂, and N₂ are one option. The gasanalyzers 18 and 16 measure the fractional concentrations of CO₂ and O₂at the mouth throughout the breath. The pressure transducer 14 is usedfor end-tidal detection. The computer runs a software implementation ofa pulmonary blood flow measurement algorithm and demands the requiredmixtures from the blender 22. The monitor may display the real-timecapnograph, oxigraph, pulmonary blood flow, and mixed-venousconcentration of CO₂.

{dot over (Q)}_(calc)={dot over (Q)}_(est)+k(FETCO_(2,B)−FETCO_(1,T))k>0  EQUATION 3a2

CvCO_(2,calc)=CvCO_(2,est) −k(FETCO_(2,B)−FETCO_(2,T))k>0  EQUATION 3b2

DESCRIPTION OF FIGURES FIG. 4

1 The initial pulmonary blood flow or mixed-venous CO₂ estimate is takenas the middle of the normal published range for the age, height, weight,and sex of the subject. Alternatively, the initial pulmonary blood flowor mixed-venous CO₂ estimate can be arbitrary. Alternatively, pulmonaryblood flow can be estimated as 0.07 L/min/kg of subject body weight.Alternatively, the initial pulmonary blood flow or mixed-venous CO₂estimate can be obtained from a pervious execution of the recursivealgorithm. Alternatively, the initial pulmonary blood flow ormixed-venous CO₂ estimate can be obtained from another measurementtechnique (thermodilution, mixed-venous blood gases). Alternatively, themixed-venous partial pressure of CO₂ can be estimated as 6 mmHg abovethe resting end-tidal CO₂ and converted to a concentration via the CO₂dissociation curve.

2 In the baseline phase, the fractional concentration of CO₂ in the G1gas (FICO_(2,gl,R)) is set and held constant. Although not necessary,FICO_(2,gl,R) is usually zero.

The G1 gas flow during the rest phase ({dot over (V)}_(gl,R)) is usuallyset to about 80% of the subjects total measured or estimated minuteventilation. In general, {dot over (V)}_(gl,R) should be low enough topermit rebreathing which at least fills the subject's anatomical deadspace, but high enough to prevent hypercapnia.

3 The baseline phase can be ended when end-tidal CO₂ is stable.Stability of end-tidal CO₂ can be determined by the standard-deviationof end-tidal CO₂ measured over five breaths being within ±2 mmHg, or ifthe difference between the largest and smallest end-tidal CO₂ measuredover the last 5 breaths is within ±2 mmHg, or if the slope of the linearregression line passing through the end-tidal CO₂ of the last fivebreaths is less than ±0.5 mmHg/breath. Alternatively, the baselineperiod can be ended after predefined time has elapsed and/or predefinednumber of breaths has occurred.

4 At the end of the baseline phase, the end-tidal CO₂ during thebaseline phase (FETCO_(2,R)) is converted to an arterial concentration(CaCO₂). The end-tidal CO₂ from the last breath of the baseline phasecan be used as FETCO_(2,R). Alternatively, FETCO_(2,R) can be theaverage of a number of breaths at the end of the baseline phase.

5 The baseline minute volume of expired CO₂ ({dot over (V)}CO_(2,R)) iscalculated from EQUATION 4, using the average end-tidal O₂ (FETO_(2,R))measured during the baseline phase, {dot over (V)}_(gl,R), FICO_(2,gl,R)FIO_(2,gl), and FETCO_(2,R).

6 The mixed-venous concentration of CO₂ is estimated from EQUATION 6ausing an estimate of the pulmonary blood flow ({dot over (Q)}_(est)),{dot over (V)}_(gl,R), FICO_(2,gl,R), FIO_(2,gl), FETCO_(2,R),FETO_(2,R), and CaCO_(2,R). Alternatively, the pulmonary blood flow isestimated starting from an estimate of the mixed-venous concentration ofCO₂ (CvCO_(2,est)) using EQUATION 6b with {dot over (V)}_(gl,R),FICO_(2,gl,R) FIO_(2,gl) FETCO_(2,R), FETO_(2,R), and CaCO_(2,R).

7 To transition from the baseline phase to the test phase, the inspiredfraction of CO₂ in the G1 gas is increased substantially for one bolusbreath, inducing a sharp increase in the end-tidal CO₂. In oneembodiment, the bolus breath increases end-tidal CO₂ by approximately 10mmHg to provide sufficient measurement resolution and minimizediscomfort to the patient. The inspired fraction of CO₂ in the bolusbreath (FICO_(2,gl,B)) required to elevate end-tidal CO₂ byapproximately 10 mmHg can be calculated using an approximation of thesubject's functional residual capacity (FRC), respiratory rate (RR),{dot over (V)}_(gl,R), and FETCO_(2,B) using EQUATION 8. The FRC can beestimated or obtained from normal published ranges for the age, weight,and sex of the subject. Respiratory rate can be measured or estimated.For most adults, FICO_(2,gl,B) of 15-20% should provide an adequateincrease in end-tidal CO₂.

EQUATION  8${{FI}{CO}}_{2,{g\; 1},B} = \frac{{RR} \cdot \left\lbrack {{\left( {{{FET}{CO}}_{2,R} + \frac{10}{{PB} - 47}} \right)\left( {{FRC} + \frac{{\overset{.}{V}}_{g\; 1}}{RR}} \right)} - {{FRC} \cdot {{FET}{CO}}_{2,R}}} \right\rbrack}{{\overset{.}{V}}_{{g\; 1},R}}$

8 The elevated end-tidal CO₂ (FETCO_(2,B)), and corresponding arterialCO₂ (CaCO_(2,B)) measured in the exhalation immediately followinginspiration of the bolus are recorded. This recorded value representsthe test concentration of CO₂ sought to be maintained in the test phase.

9 Subsequently, the inspired fraction of CO₂ (FICO_(2,gl,T)) and G1 flowrate ({dot over (V)}_(gl,T)) during the test phase are set to try andmaintain end-tidal CO₂ at FETCO_(2,B)·{dot over (V)}_(gl,T) can bechosen arbitrarily, but in general, {dot over (V)}_(gl,T) should be lowenough to permit rebreathing which at least fills the subject'sanatomical dead space. EQUATION 7a, with {dot over (Q)}_(est),CvCO_(2,est), {dot over (V)}_(gl,T), FIO_(2,gl), FETCO_(2,B),FETO_(2,TR), and CaCO_(2,B), can be used to calculate FICO_(2,gl,T)presumed to force a second steady state of end-tidal CO₂ at FETCO_(2,B).Alternatively, FICO_(2,gl,T) can be set arbitrarily within thelimitations of the hardware and EQUATION 7b, with {dot over (Q)}_(est),CvCO_(2,est), FICO_(2,gl,T), FIO_(2,gl), FETCO_(2,B), FETO_(2,R), andCaCO_(2,B), can be used to calculate {dot over (V)}_(gl,T) presumed toforce a second steady state of end-tidal CO₂ at FETCO₂₃.

10 This {dot over (V)}_(gl,T) and FICO_(2,gl,T) is delivered untilrecirculation is detected (described later), or for a predefined lengthof time presumed to be less than the recirculation time, or a predefinednumber of breaths presumed to occur before recirculation.

11 At the end of the test phase, the end-tidal CO₂ during the test phase(FETCO_(2,T)) is converted to an arterial concentration (CaCO_(2,T)).The end-tidal CO₂ from the last breath of the test phase can be used asFETCO_(2,T). Alternatively, FETCO_(2,T) can be the average of a numberof breaths at the end of the test phase.

12 The minute volume of expired CO₂ during the test phase ({dot over(V)}CO_(2,T)) is calculated from EQUATION 4, using the average end-tidalO₂ (FETO_(2,T)) measured during the test phase, {dot over (V)}_(gl,T),FICO_(2,gl,T), FIO_(2,gl), and FETCO_(2,T). Pulmonary blood flow andmixed-venous CO₂ are recalculated ({dot over (Q)}_(calc), CvCO_(2,calc))from EQUATIONS 3a1,b1 using {dot over (V)}CO_(2,R), CaCO_(2,R), {dotover (V)}CO_(2,T), and CaCO_(2,T) or EQUATIONS 3a2,b2 using {dot over(Q)}_(est), CvCO_(2,est), FETCO_(2,B), and FETCO_(2,T). Subsequently,the system is returned to the baseline state.

This manoeuvre is repeated utilizing either the calculated pulmonaryblood flow of each test as the estimated pulmonary blood flow in thenext iteration, or the calculated mixed-venous CO₂ concentration as theestimated mixed-venous CO₂ concentration in the next iteration.

13 Testing is terminated when the difference in pulmonary blood flowcalculated between subsequent tests differs in magnitude less than auser-definable threshold. Optionally, the algorithm can be continuedindefinitely. Optionally, the algorithm can be executed for a predefinednumber of iterations.

FIG. 1

According to one embodiment of a gas delivery system, the systemapparatus is shown in FIG. 1. It consists of a gas blender 22, asequential gas delivery circuit 26, gas analyzers for oxygen 16 andcarbon dioxide 18, a pressure transducer 14, a computer 8 includingsoftware 10 (which is optionally embodied a computer program product)that works the gas blender 22 to request gas flows and with the gasanalyzers 16 and 18, pressure transducer 14 and input devices formeasured or estimated physiological parameters 36 and algorithm settings34 to obtain inputs as contemplated herein. The gas blender 22 may beconnected to three pressurized gas tanks 32. The gas blender optionallycontains three rapid flow controllers (not shown) capable of deliveringaccurate mixes of three source gases, optionally comprised of CO₂, O₂,and N₂ to the circuit. The concentrations of CO₂, O₂, and N₂ in thesource gases must be such that they can produce the blends required tocarry out the algorithm. Pure CO₂, O₂, and N₂ are one option. The gasanalyzers 18 and 16 measure the fractional concentrations of CO₂ and O₂at the mouth throughout the breath. The pressure transducer 14 is usedfor end-tidal detection. The computer runs a software implementation ofa pulmonary blood flow measurement algorithm and demands the requiredmixtures from the blender 22. The monitor may display the real-timecapnograph, oxigraph, pulmonary blood flow, and mixed-venousconcentration of CO₂.

Other inputs to the algorithm include an initial estimate of pulmonaryblood flow or mixed-venous CO₂ 36, and termination criteria for thealgorithm 34.

FIG. 5 Panel A

In FIG. 5a (Panel A), three iterations of the recursive algorithmshowing convergence of the calculated pulmonary blood flow to the actualpulmonary blood flow starting from an incorrect estimate. As shown, ifthe estimated pulmonary blood flow is incorrect, the predicted transferrate of CO₂ between the circulation and the alveolar space will also bein error. However, the minute volume of expired of CO₂ in the test phasewill exponentially equilibrate with the flux across the blood-alveolarinterface. As a result, the pulmonary blood flow calculated in each testwill better reflect the actual pulmonary blood flow ({dot over(Q)}_(act)) than the ingoing estimate. Because this procedure isimplemented recursively, and the estimated parameters updated after eachiteration to reflect the previously calculated values, the algorithmconverges to the actual physiological parameters of the subject.

The rate at which the calculated parameters converge to the actualparameters depends on how fast the end-tidal CO₂ approaches equilibriumin the test phase. The derivative of an exponential function is largestat the start and vanishes with time. Therefore, a substantial refinementin the estimated parameters occurs in the breaths before recirculation.As a result, the calculated parameters at the end of each test aresignificantly more accurate than the previous estimates.

Panel B

FIG. 5B (Panel B) shows that (a) if the estimate of pulmonary blood flowis higher than the actual pulmonary blood flow, the end-tidal CO₂ in thetest phase drifts exponentially upwards; (b) if the estimate ofpulmonary blood flow is lower than the actual pulmonary blood flow, theend-tidal CO₂ in the test phase drifts exponentially downwards; (c) ifthe estimate of pulmonary blood flow is approximately equal to than theactual pulmonary blood flow, the end-tidal CO₂ in the test phase remainsconstant. It also shows how recirculation may be detected by analysis ofthe time course of the end-tidal CO₂ during the test phase. Prior torecirculation, the end-tidal CO₂ approaches a steady valueexponentially—the absolute difference between consecutive end-tidalmeasurements decreases as the test proceeds. Recirculation causes adeviation from this asymptotic approach, detectable as an increase inthe difference between consecutive end-tidal CO₂ measurements.Mathematically, this is shown in equation 9.

REFERENCES

-   [1] Geerts B F, Aarts L P, Jansen J R. Methods in pharmacology:    measurement of cardiac output. Br J Clin Pharmacol. 2011 March;    71(3):316-30.-   [2] Fick A. Ueber die Messung des Blutquantums in den    Herzventrikeln. Sitzungsberichte der Physiologisch-Medizinosche    Gesellschaft zuWuerzburg 1870; 2: 16.-   [3] Douglas A R, Jones N L, Reed J W. Calculation of whole blood CO2    content. J Appl Physiol. 1988 July; 65(1):473-7.-   [4] Kelman R G. Digital computer procedure for the conversion of    PCO2 into blood content. Respir Physiol 3: 111-115, 1967.-   [5] DEFARES J G. Determination of PvCO2 from the exponential CO2    rise during rebreathing. J Appl Physiol. 1958 September;    13(2):159-64.-   [6] COLLIER C R. Determination of mixed venous CO2 tensions by    rebreathing. J Appl Physiol. 1956 July; 9(1):25-9.-   [7] Gedeon, A., Forslund, L., Hedenstierna, G., Romano, E. (1980). A    new method for noninvasive bedside determination of pulmonary blood    flow. Med Biol Eng Comput 18(4), 411-8.-   [8] Jaffe M B. Partial CO2 rebreathing cardiac output—operating    principles of the NICO system. J Clin Monit Comput. 1999 August;    15(6):387-401.-   [9] Tachibana K, Imanaka H, Takeuchi M, Takauchi Y, Miyano H,    Nishimura M. Noninvasive cardiac output measurement using partial    carbon dioxide rebreathing is less accurate at settings of reduced    minute ventilation and when spontaneous breathing is present.    Anesthesiology. 2003 April; 98(4):830-7.-   [10] Yem J S, Tang Y, Turner M J, Baker A B. Sources of error in    noninvasive pulmonary blood flow measurements by partial    rebreathing: a computer model study. Anesthesiology. 2003 April;    98(4):881-7.-   [11] Somogyi R B, Vesely A E, Preiss D, Prisman E, Volgyesi G, Azami    T, et al. Precise control of end-tidal carbon dioxide levels using    sequential rebreathing circuits. Anaesth Intensive Care 2005    December; 33(6):726-32.

1. A method of controlling a gas delivery apparatus to deliver a testgas (TG) for non-invasively determining a subject's pulmonary blood flowcomprising the steps of: (a) Using an iterative algorithm to control atleast one apparatus controllable variable to test one or more testvalues for an iterated variable by: A) obtaining input of a steady statevalue of an end tidal test gas concentration and a corresponding valueof at least one apparatus controllable variable for use in the iterativealgorithm; B) providing an inspired concentration of a test gas thatachieves a test concentration of the test gas in the subject's end tidalexhaled gas; C) using a test value of the iterated variable in theiterative algorithm to set the gas delivery apparatus to deliver, for atleast one series of inspiratory cycles, an inspiratory gas comprising atest gas that is computed to maintain the test concentration of the testgas in the subject's end tidal exhaled gas; D) obtaining inputcomprising measurements of end tidal concentrations of test gas forexpiratory cycles corresponding to the at least one series ofinspiratory cycles and a corresponding value of at least one apparatuscontrollable variable for use in the iterative algorithm; E) using atleast one measurement obtained in step D) as a reference end tidalconcentration value to generate at least one of the following outputs:(1) the test value satisfies a test criterion; (2) a refined test value;wherein the reference end tidal concentration is a surrogate steadystate value and the reference end tidal concentration is used to refinethe test value; (b) If output (1) is not obtained, repeating step (a) asnecessary at least until output (1) is obtained; and (c) If output (1)is obtained, outputting a value for pulmonary blood flow which, based onthe test criterion, sufficiently represents a subject's true pulmonaryblood flow.
 2. A method according to claim 1, wherein the reference endtidal concentration is the last measurement obtained prior to arecirculation or an average of such last measurements.
 3. A methodaccording to claim 2, wherein the test gas is carbon dioxide.
 4. Amethod according to claim 1, wherein the iterative algorithm ischaracterized in that it defines a mathematical relationship between theat least one apparatus controllable variable, the iterated variable andthe end tidal concentration of test gas attained by setting theapparatus controllable variable, such that the iterative algorithm isdeterminative of whether iteration on the test value satisfies a testcriterion or iteratively generates a progressively refined test value.5. A method according to claim 1, wherein the iterative algorithmemploys a test mathematical relationship based on the Fick equation. 6.A method according to claim 5, wherein the refined test value isascertained based on the differential Fick equation.
 7. A methodaccording to claim 1, wherein the apparatus controllable variable is theinspired concentration of test gas in the inspiratory gas.
 8. A methodaccording to claim 1, wherein the apparatus controllable variable israte of flow of test gas containing inspiratory gas into the circuit,where the rate of flow is determinative of the alveolar ventilation. 9.A method according to claim 1, wherein the iterated variable is selectedfrom the group consisting of pulmonary blood flow, a variable determinedby pulmonary flow from which pulmonary blood flow can be mathematicallycomputed, and a mixed venous concentration of test gas.
 10. A gasdelivery system adapted to deliver a test gas (TG) for non-invasivelydetermining a subject's pulmonary blood flow comprising: A gas deliveryapparatus; A control system for controlling the gas delivery apparatusincluding at least one apparatus controllable variable to test one ormore test values for an iterated variable, the control system comprisinga computer for executing an iterative algorithm, the gas delivery systemincluding means for: A) Obtaining input of a steady state value of anend tidal test gas concentration and a corresponding value of at leastone apparatus controllable variable for use in the iterative algorithm;B) providing an inspired concentration of a test gas that achieves atest concentration of the test gas in the subject's end tidal exhaledgas; C) using a test value of the iterated variable in an iterativealgorithm to set the gas delivery apparatus to deliver, for at least oneseries of inspiratory cycles, an inspiratory gas comprising a test gasthat is computed to maintain the test concentration of the test gasbased a test value of the iterated variable; D) obtaining inputcomprising measurements of end tidal concentrations of test gas forexpiratory cycles corresponding to the at least one series ofinspiratory cycles; E) using at least one measurement obtained in stepC) as a reference end tidal concentration value to generate at least oneof the following outputs: (1) the test value satisfies the testcriterion; (2) a refined test value; wherein the reference end tidalconcentration is a surrogate steady state value and is used to generatethe refined test value; wherein the iterative algorithm uses at leastone apparatus controllable variable to iteratively test one or more oftest values for the iterated variable based on the following criteria:If output (1) is not obtained, repeating steps (B) to (E) as necessaryat least until output (1) is obtained; and If output (1) is obtained,outputting a value for pulmonary blood flow which, based on the testcriterion, sufficiently represents a subject's true pulmonary bloodflow.
 11. A gas delivery system according to claim 10, wherein the gasdelivery apparatus comprises at least one input port for receiving aninspiratory gas containing the test gas, at least one output port forconnection to a breathing circuit and a flow controller for controllingthe rate of flow of the inspiratory gas.
 12. A gas delivery systemaccording to claim 10, wherein the computer is CPU.
 13. A gas deliverysystem according to claim 10, wherein reference end tidal concentrationis the last measurement obtained prior to a recirculation or an averageof such last measurements.
 14. A gas delivery system according to claim10, wherein the test gas is carbon dioxide.
 15. A gas delivery systemaccording to claim 10, wherein the iterative algorithm is characterizedin that it defines a mathematical relationship between the at least oneapparatus controllable variable, the iterated variable and the end tidalconcentration of test gas attained by setting the apparatus controllablevariable, such that the iterative algorithm is determinative of whetheriteration on the test value satisfies a test criterion or iterativelygenerates a progressively refined test value.
 16. A gas delivery systemaccording to claim 15, wherein the iterative algorithm employs a testmathematical relationship based on the Fick equation.
 17. A gas deliverysystem according to claim 10, wherein the apparatus controllablevariable is the inspired concentration of test gas in the inspiratorygas.
 18. A gas delivery system according to claim 10, wherein theapparatus controllable variable is rate of flow of test gas containinginspiratory gas into the circuit, where the rate of flow isdeterminative of the alveolar ventilation.
 19. A method according toclaim 10, wherein the iterated variable is selected from the groupconsisting of pulmonary blood flow, a variable determined by pulmonaryflow from which pulmonary blood flow can be mathematically computed, anda mixed venous concentration of test gas.
 20. A computer program productcomprising a non-transitory computer readable medium encoded withprogram code for controlling the operation of gas delivery apparatusincluding at least one apparatus controllable variable, the program codeincluding code for iteratively generating and evaluating test values ofa iterated variable based on an iterative algorithm in order output atest value of the iterated variable that meets a test criterionincluding program code for: A) Obtaining input of a steady state valueof an end tidal test gas concentration and a corresponding value of atleast one apparatus controllable variable for use in the iterativealgorithm; B) providing an inspired concentration of a test gas thatachieves a test concentration of the test gas in the subject's end tidalexhaled gas and using the test value of the iterated variable in theiterative algorithm to set the gas delivery apparatus to deliver, for atleast one series of inspiratory cycles, an inspiratory gas comprising atest gas that is computed to maintain the test concentration of the testgas; C) obtaining input comprising measurements of end tidalconcentrations of test gas for expiratory cycles corresponding to the atleast one series of inspiratory cycles; D) using at least onemeasurement obtained in step C) as a reference end tidal concentrationvalue to generate at least one of the following outputs: (3) the testvalue satisfies the test criterion; (4) a refined test value; whereinthe reference end tidal concentration is a surrogate steady state valueand is used to obtain the refined test value; wherein the iterativealgorithm uses at least one apparatus controllable variable toiteratively test one or more of test values for the iterated variablebased on the following criteria: If output (1) is not obtained,repeating step (B) to (D) as necessary at least until output (1) isobtained; and If output (1) is obtained, outputting a value forpulmonary blood flow which, based on the test criterion, sufficientlyrepresents a subject's true pulmonary blood flow.